Gear Box. WRIG. Turbine Blade. PCC. Grid. ~. Wind β r Ï m Ï e. T. Figure 3. WECS .... speed by the rotor blade of a wind turbine can be expressed as ... the blade radius of the turbine;. Vw ... A wind turbine is typically designed to extract the ...... (45). Eq. (45) changes into: 2 .ref. 1. (S. ) . dc dc dc dc. P. I dc dc. P. I dc dc dc.
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com
Modeling for Development of Simulation Tool: A Case Study of GridConnected Doubly Fed Induction Generator Based on Wind Energy Conversion System 1
Le Van Dai1 and Doan Duc Tung2,* Facuty of Electrical Engineering, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam. 2 Department of Engineering and Technology, Quy Nhon University, Binh Dinh, Vietnam. * Corresponding author ORCID: 0000-0001-9312-002, 2ORCID: 0000-0002-7560-1607
1
The wind turbine is one of the most important components in wind energy conversion system (WECS) that converts the kinetic energy of the incoming wind into electricity or other forms of energy. A wide diversity of wind turbine technologies has been used over the years, three groups of wind turbines have been developed based on operation either with a fixedspeed or variable-speed [1], which include the following:
Abstract The motive of this paper is to build a mathematical model of doubly fed induction generator based on wind energy conversion system (DFIG-WECS). This motivation comes from the grid-connected performances analysis of the distributed generators (DGs) installed in the renewable energy conversion system Lab at Quy Nhon University. The main objective is to develop a textbook model for controlling the DFIG-WECS that is independent on the standardized manufacturer. Typical model of manufacturer are more detail and exactitude, but here is the difficulty concerned with the agreements of monopolization and non-disclosure. Therefore, this model became an issue for research purposes. The DFIGWECS is the most commonly used the WESC because of its advantages, so that it installed in the renewable energy lab for the research and study. The entire turbine-generator system is implemented in PSCAD/EMTDC, in which the proportionalintegral (PI) controllers are used for the control loops of both the rotor side converter (RSC) and grid side converter (GSC). The parameters of PI controllers are calculated based on the Butterworth polynomial method. The effectiveness of the proposed model is verified via time domain simulation of a 2.0 MW-575 V DFIG-WECS under different operating conditions. Simulation results show that the proposed model provides a good software simulation test bed, and it can be used for the research purposes on distributed generation issues and further research.
Group A: Fixed-speed wind turbines with power converter interface. The fixed speed wind turbine system consists of a squirrel cage induction generator (SCIG), a soft starter, and a capacitor bank, as shown in Fig. 1, in which the SCIG is directly connected to the grid through a step up transformer. The soft starter is used to limit high inrush currents during system start up, but a bypass switch bypasses this soft starter after the started system. The capacitor bank is usually required to compensate the reactive power drawn by the generator. This system has advantages, such as simple electrical system, moderate manufacturing and maintenance costs, and high reliable operation. However, it also has some disadvantages. For example, the out power cannot be adjusted, leading to fluctuated output power due to varied wind speed, causing voltage fluctuation, and the flicker effects in the case of weak grid. Presently, despite such disadvantages, this WECS system is still widely accepted. Wind
t
Gear Box
Bypass switch and soft starter
Te
Transformer
m
Keywords: Doubly fed induction generator (DFIG), wind energy conversion system (WECS), distributed generator (DG), Butterworth polynomial method, grid-connected performance analysis
Grid
~
PCC SCIG
Turbine Blade Capacitor bank
Figure 1: The wind energy conversion configuration without power converter interface.
system
(WECS)
Group B: Variable-speed wind turbines with reduced capacity converter. For this group, it can be divided into two types based on the power rating of the power electronic converter. The first type is limited variable-speed with variable rotor resistance. This type of turbine has a small operation range of 10% above the synchronous speed of the generator, which depends on variable generator rotor resistance [2], as shown in Fig. 2, in which the system uses a wound rotor induction generator (WRIG) with a variable additional rotor resistance, which is controlled by power electronics. In addition, a soft starter is needed to reduce the inrush current and a capacitor bank is
INTRODUCTION In recent years, the energy resources, such as the wind, solar, photovoltaic, biomass, etc. have become the important renewable energy resources for the existing and future electrical energy demand all over the world. This is due to the growing demand of environmental, economic, and political concerns of electrical energy production using fossil fuels. Along these energy resources, the wind energy generation has become one of the most promising future energy resources for the total energy production.
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com also instated to compensate the reactive power demand of generator. With such idea, the output power and slip can be controlled, so the system can capture more energy from the wind energy. WRIG Wind
r
Gear Box
Te
Bypass switch and soft starter
Transformer
this WECS. In many cases, the PMSG is considered as a good option to be used in WECS because it does not require energy supply for excitation, it can operate without the need of a gearbox if WECS uses a low speed synchronous generator with a large number of poles or salient pole. As such, the efficiency of the system is improved, and the initial costs and maintenance costs are reduced. However, its major drawback is that it very sensible to the temperature and it can lose magnetic properties if exposed to high temperatures. During the last few years, any large companies like Vestas Wind Systems, GE Energy, and Alstom Pure Torque, their production are based on the second type of group B. Besides, this wind turbine concept has advantages as above-mentioned compared with other ones, whereas it has drawback to be very sensitive to the grid disturbances, especially under the voltage dips. For example, when an external grid fault occurs, a voltage dip is produced at the generator terminal, resulting in over-voltages and -currents in the rotor and stator circuits and the over-voltages in the DC-link, so that the generator turbine system cannot remain connected to the grid during a fault. This is incentive by the fact that disconnecting a large amount of wind power generation can cause the instability of the power system. Therefore, this WECS configuration based on WRIG will be chosen to perform the purposes of this study.
Grid ~
m
PCC
Turbine Blade Variable resistance
Capacitor bank
Figure 2. WECS configuration with variable rotor resistance.
Therefore, the WECS to this configuration has advantages, such as the simple circuit, moderate manufacturing and maintenance costs, reliable, and reduction of mechanical load and power fluctuations. However, it also has some disadvantages. For example, the speed range depends on the size of the variable rotor resistance, the power is dissipated in the variable resistance, and the control of reactive and active is poor. As to the second type of group B, it known as the doubly fed induction generator (DFIG), which includes a WRIG and a grid connected power converter system, as shown in Fig. 3. For this configuration, the soft starter or capacitor bank does not use, whereas the power converters are applied. The use of the power converters allow bi-directional power flow in the rotor circuit and increases the range of the dynamic speed control of the generator, which extends a range of 30% around the synchronous speed [3]. The size of the power converters is approximately 30% of the rated power of the generator, so that the cost of the power converters reduces in comparison with the wind energy systems using full-capacity converters. DFIG Wind
r
Gear Box
Te m
Transformer
WRIG
WRSG/SCIG/PMSG Wind
Turbine Blade
Gear Box
Te
Transformer
Grid ~
m Full capacity power converters
PCC
Figure 4. WECS configurations with full capacity converters
In general, the wind turbine-generator model includes submodels, such as the wind source, aerodynamic, drive train, generator, and control system, as shown in Figs 1-4. In the prehistory of wind power development, most wind turbinegenerators were used with the induction generators and fixedspeed wind turbines. Since electric generators can only operate at a constant speed, the generated power efficiency is low for most wind speeds. Recently, with the fast growth of wind energy industry, the effects on the transient stability of the electric grid are very serious when they generated the power to the grid. Currently, the wind turbine-generator systems based on the DFIGs are controlled using the back-to-back electric power converters, accounting for around 50% of the installed wind farms worldwide in on-shore and off-shore applications [4]. Therefore, several researchers proposed DFIG-WECS models to study the impact of its integration into the grid and identify the main issues as the variable speed, power quality, voltage and reactive power control, frequency synchronization, harmonics, grid-interconnected control [510]. Ledesma et. al [11] has introduced simulation models for transient stability studies, Lei el. al [12] has proposed a DFIG wind turbine model for the grid integration studies, and Sun el.al [13] has developed a DFIG wind turbine model for transient analysis of grid-connected after an external short-circuit fault. It is observed that the most of existing methods in the previous literatures have been proposed recently models to study and solve particular problems. These models are no a textbook
Grid ~
Partial scale frequency converter
r
PCC
Turbine Blade
Figure 3. WECS configuration with reduced capacity converters.
The advantages of this WECS configuration include, for instance the power conversion efficiency is improved, generator speed range is extended, and dynamic performance is enhanced in comparison with the fixed speed and variable resistance WECS. However, its major drawback is very sensitive to abrupt changes in their terminal voltage and need to use the additional protection in the case of grid fault. Group C: Variable-speed wind turbines with full capacity converter. Another promising WECS configuration that is becoming popular for the new installed wind turbines, as shown in Fig. 4, in which the generator is connected to the power grid through the back-to-back voltage source converter with a common DC-link (full capacity converters). Many machines like the wound rotor synchronous generator (WRSG), squirrel cage induction generator (SGIG), and permanent magnet synchronous generator (PMSG) have all found applications in 2982
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com model for controlling the DFIG-WECS that is independent on the standardized manufacturer, which can be used as a testbench for academic and further research purposes. This paper proposes a mathematical model DFIG-WECS suitable for grid integration studies based on the vector control technique, the PI controllers are designed based on the Butterworth polynomial method. The presented model is easy to integrate with other electric components as solar, photovoltage, other distributed generator (DG). It is a simulation tool used to model and study the transient behaviors of offshore, micro-grid, and standalone systems. The motivation comes from the grid-connected performance analysis of the distributed generators (DGs) installed in the renewable energy conversion system Lab at Quy Nhon University. The objective of this work is to develop a textbook model for controlling the DFIG-WECS that is independent on the standardized manufacturer. The main new contribution of this paper is to present a textbook model can be used as a test-bench for academic and further research purposes. The remainder of this paper is organized as follows: Section 2 addresses the mathematical model of wind turbine-generator model. Section 3 establishes the wind turbine-generator control system. The case studies and conclusions are given in Section 4 and 5, respectively. Finally, the tested system parameters are listed out in the Appendix.
Table 1: The coefficients of ij for i,j = 0, 1, ..., 4. i/j 0 1 2 3 4
Vwind
Vwind
Aerodinamic Torque
Cp
C p ( , )
Pitch angle
r
Rotor speed
Figure 5. The block diagram of the aerodynamic model.
Fig. 6a shows a plot of the change Cp(.) versus the tip speed ratio with different pitch angles. Observing this figure, at low wind speed to medium one, the pitch angle is controlled to allow the wind turbine to be operated at its optimal conditions. At high wind speed, the pitch angle is adjusted to spill some of the aerodynamic energy. It could also be able to see from this Fig. 6a, at the optimal point, opt is equal to 8.1 and is equal to zero, maximal power coefficient is equal 0.48. A wind turbine is typically designed to extract the maximal wind energy possible at wind speeds in a range 1015 m/s. At wind speeds beyond 15 m/s, the wind turbine can spill some of the energy and completely cut out at wind speeds over 2025 m/s. (8.1,0.48) 0.5
Power coefficientC p ( , )
0
0.4
5
0.3
10
0.2
15
(4)
0.50 0.25
4(m/s)A
1.00
0.00
Zone_1 0.0
2
B
10.0
2983
8
10
12
(a)
12(m/s) Zone_3 15.0
Wind speed (m/s) (b)
where the air density; R the blade radius of the turbine; Vw the wind speed; the tip speed ratio; the blade pitch angle; the rotor angular speed of the turbine wind; and t the coefficients are given in Table 1 [15]. ij
6
Tip speed ratio
20.0
Zone_4 25.0
14
16
Operational speed range
2.0
D
C
Zone_2 5.0
4
Power limitation
Rated wind speed
(3)
1.50
0
C@D
1.5
1.0
0.5
0
B A 0.1
0.3
0.5
0.7
0.9
Generator speed (p.u.) (c)
1.1
Max. rotor speed
Power optimization
2.00
Cut-out wind speed
(2)
20
Rated rotor speed
25
0
Min. rotor speed
0.1
Electrical power (MW)
R t , Vw
Pm
r
Low limit wind speed
i 0 j 0
4 1.1524e-5 -2.3895e-5 2.7937e-6 -8.9194e-8 4.9686e-10
Mechanical power is developed by the wind turbine rotor
Cut-in wind speed
4
3 -1.3365e-4 1.0683e-3 -1.4855e-4 5.9924e-6 -7.1535e-8
Wind speed
Tm
Mechanical power (MW)
4
Pm
r
Pwind
The power coefficient is a nonlinear function of the blade pitch angle and the tip speed ratio , we have:
ij i j ,
2 -1.2406e-2 -1.3934e-2 2.1495e-3 -1.0479e-4 1.6167e-6
Aerodinamic model
Aerodynamic model The energy production of wind turbine depends on the coaction between the turbine rotor and the wind velocity. The energy flow under motion in the form of air affects the blades of wind turbine rotor to convert into rotational energy under a mechanical form, which drives the electric generator, and then it converts into electrical energy. The relationship between the wind power swept and wind speed by the rotor blade of a wind turbine can be expressed as [14,15]: 1 (1) Pw R2Vw3 , 2 The mechanical power transferred to the wind turbine rotor is reduced by the power coefficient as follows:
C p (, )
1 2.1808e-1 6.0405e-2 -1.0996e-2 5.7051e-4 -9.4839e-6
The block diagram of the aerodynamic model defined in the Eq. (2), as shown in Fig. 5.
WIND TURBINE-GERNERATOR MODEL
Pm PwC p (, ).
0 -4.1909e-1 -6.7606e-2 1.5727e-2 -8.6018e-4 1.4787e-5
1.3
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com Figure 6. Three static curves are used in the design of the doubly fed induction generator based on wind energy conversion system (DFIG-WECS): (a) Power coefficient curves versus tip speed ratio for various pitch angles; (b) Wind turbine power curve versus variable-speed wind; and (c) Electrical power curve versus generator speed.
d t Tt Tg Dt t , dt d g Jg Tg Tt Dg g , dt dTg d d g K tg (t g ) Dtg ( t ), dt dt dt t N g g , Jt
As can be observed from Eq. (4), the tip speed ratio of a wind turbine varies over a wide range depending on the wind speed. However, the power production from a wind turbine can be maximized if the turbine is operated at maximal power coefficient of Cp(.), as shown in Eq. (2); in order to achieve this objective, the rotor speed of wind turbine should be adjusted according to the wind speed. Therefore, the variable speed WECS based on DFIG technology is only capable of doing this. The rotor speed can be controlled using the dynamic pitch angle on porpoise for controlling the difference between extracted power from the wind turbine and the out electrical power. A detailed development of dynamic pitch control will be analysed in the next sections.
where Jt the wind turbine inertia constant; Jg the generator inertia constant; Tt the wind turbine torque; Tg the generator turbine torque; Dt the friction coefficient of turbine; Dg the friction coefficient of generator; Dtg the flexible coupling; Ktg the spring constant; g the generator mechanical speed; t the wind turbine mechanical speed; and Ng the gearbox radio. Assuming that the shaft stiffness and the damping factor between the wind turbine and the generator are neglected, the two-masses drive train model reduces to a one-mass one, and the electromechanical dynamic can be described as follows [18]: d m J Tm Te C f m , dt (6) P Tm m , m where m the mechanical speed of the shaft turbine; Cf the friction factor of the system; J the total constant; Tm the shaft mechanical torque; and Te the electromagnetic torque.
Drive Train Model The electric generator is used in the wind turbine system that is driven by the wind turbine through a gearbox system to obtain a suitable speed range. Using the gearbox, the low rotational speed of the wind turbine rotor is transformed into high rotation speed on the generator rotor. The gearbox ratio of 70.0100.0 is common for the wind turbine 2.03.0 MW [16]. The gearbox ratio is actually selected under the consideration of the range of the demand of the operating speed of the electric generator that is chosen based on the actual wind speed and the size of the power converter. In order to investigate the effects of WECS when connecting to the grid, the mechanical system is used to represent dymamic stability of DFIG-WECS to be a two-mass model, as shown in Fig.7, including a low-speed one of the wind turbine and a high-speed one of the generator. All the magnitudes are considered in the fast shaft (shaft of generator). The turbine rotor inertia Jt is driven by its torque Tt at speed t and the generator inertia Jg is driven by its electromagnetic torque Tg at speed g. The stiffness and damping coefficients, Ktg and Dtg are the flexible coupling between generator and wind turbine inertias. Dt and Dg are respectively the friction coefficients of wind turbine and generator, which denote the mechanical losses by the friction in the rotational movement.
Generator model The DFIG-WECS utilizes the electric generator that is a WRIG, in which the stator windings is directly connected to the power grid, whereas the rotor windings connection to the grid to be performed through the back-to-back converters, which are a rotor-side converter (RSC) and a grid-side converter (GSC) via slip rings. Therefore, the DFIG can absorb or deliver power from the grid via the rotor windings through these RSC and GSC, whereas the injection of power into the grid is done through the stator windings. However, the power flow in the rotor circuit depends on operating conditions [19]. In this section, we deal with the development of a mathematical model of DFIG based on WECS. Fig. 8 plots an example of the torque versus speed characteristics of DFIG wind generator. As shown in this figure, the DFIG can operate in both generator and motor operation with a rotor speed range of max around the synchronous speed s. Depending on the rotor speed, there are two modes of operation in a DFIG generator, in which the DFIG operates above the synchronous s to be called the super-synchronous mode and it operates below the synchronous speed to be called sub-synchronous. The slip
Wind Turbine Rotor
Jt
Low speed shaft
High speed shaft
t
Tt Dt
Electric Generator Rotor
K tg Gearbox
Ng
Dtg
g J g
Tg
(5)
Dg
Figure 7. Two-mass drive train model of wind turbine system. The dynamic equations of the wind turbine in the fast shaft are expressed as [17]:
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com ratio is negative in the super-synchronous mode, the DFIG operates like the motor and becomes positive in the subsynchronous mode, and the DFIG operates like the generator. Fig. 9 plots the power flow in the DFIG wind turbine system [20]; the rotor circuit can receive or deliver power from or to the grid, depending on whether the slip is positive or negative. In the super-synchronous operating mode, the mechanical power from the shaft is delivered to the grid though both the rotor and stator of the generator, as shown in Fig. 9a, in which the rotor power is transferred to the grid via power converters, whereas the stator power is directly delivered to the grid. The power delivered to grid is the mechanical power, if the losses in the generator and converters are neglected.
1.0
Power [p.u.]
0.75
0.25
0.0
-0.25 1.0
0.4 0.2
0.2
Generator
s
0.0
0.0 Motor
-0.2
-0.2
-0.4
-0.4
Power [p.u.]
Torque [p.u.]
0.6
0.4
-0.6
-0.6 2max
-0.8 1.0
0.8
0.6
0.4
0.2
-0.8
0.0 -0.2 Slip ratio
-0.4
-0.6
-0.8
-1.0
Figure 8. Speed-torque characteristics of the doubly fed induction generator (DFIG) generator. WRIG
Grid
Transformer
r
Pwind
Ps
Pm
Ps Pm Pr RSC
Vwind
GSC
Pg Pm
Pr
~
PCC
(a)
r
Pm
Ps
0.0 -0.2 Slip ratio
Ls
Grid
Transformer
Pg Pm
dr ( Llr Lm ) idr Lm ids ,
~
-0.4
-0.6
-0.8
-1.0
(9)
Lr
PCC
GSC
Pr
Pr
Ps Pm Pr RSC
Vwind
0.2
qs ( Lls Lm ) iqs Lm iqr ,
r
WRIG
Pwind
0.4
Ls
Pr
0.6
Figure 10. Generated power flow of a DFIG.
Sub-synchronous Super-synchronous
0.6
0.8
The equivalent circuit of the DFIG based on the WESC is drawn in Fig. 11, in which the generator is a WRIG with slip rings rotor, as shown in Figure 11a. The ABC/abc model is well-known, can be found in [21]. A fourth-order state space model using the dq synchronous rotating reference frame can represent the dynamic behaviors of the electromagnetic parts. The voltage equations of rotor and stator can be given as [22]: d uds Rs ids qs ds , dt d qs uqs Rs iqs ds , dt (8) d uqr Rr idr ( r ) qr dr , dt d qr udr Rr iqr ( r ) dr . dt Next, equations of magnetic flux of the rotor and stator: ds ( Lls Lm ) ids Lm idr ,
0.8
0.8
0.5
qr ( Llr Lm ) iqr Lm iqs .
r
Lr
(b)
According to Eqs. (8) and (9), the current equation can be rewritten under the following form:
Figure 9. Power of an ideal DFIG: (a) Super-synchronous mode; and (b) Sub-synchronous mode.
Fig. 10 plots the generated power flow of a DFIG. As observed from this figure, the generator operates at a speed under synchronous speed, the stator is providing the power Ps and the rotor is subtracting power Pr sPs, whereas the generator operates at a speed over synchronous speed, the rotor is injecting power Pr sPs. Therefore, the generated power flow by DFIG distributed to the grid is: Pg Pm Ps Pr ;
Pr 0 super-ynchronous operating mode, (7) Pr 0 sub-synchronous operating mode, where Pm, Ps, and Pr are the mechanical, stator, and rotor powers, respectively.
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com
dids R RL L s ids r iqs r m idr r m iqr dt Ls Ls Lr Ls
3 (uds ids uqs iqs ), 2 3 Qs (uqs ids uds iqs ), 2 3 Pr (udr idr uqr iqr ), 2 3 Qr (uqr idr udr iqr ). 2 Next, the total active and reactive power is: PTotal Ps Pr , Ps
uds L m udr , Ls Ls Lr
diqs
R L RL r ids s iqs r m idr r m iqr dt Ls Ls Ls Lr
uqs Ls
Lm uqr , Ls Lr
L2 di RL L R dr s m ids r m iqs r idr r m iqr Ls Lr dt Ls Lr Lr Lr
diqr dt
r
where
(10)
(11)
(12) QTotal Qs Qr . Next, by neglecting the rotor and copper losses, the rotor active power can also be expressed from the following equation: Ps sPr . (13) Finally, the equation of electromagnetic torque can be obtained as follows: 3 (14) Te p(iqs ds ids qs ). 2
Lm u uds dr , Ls Lr Lr Lm RL L2 R ids s m iqs r m iqr r iqr Lr Ls Lr Ls Lr Lr uqr Lm uqs , Ls Lr Lr
( Ls Lr L2m ) / Ls Lr ;
Rs
r pm
uds uqs udr uqr ids iqs idr iqr Rs Rr
the d-axis stator voltage; the q-axis stator voltage; the d-axis rotor voltage; the q-axis rotor voltage; the d-axis stator current; the q-axis stator current; the d-axis rotor current; the q-axis rotor current; the stator resistance; the rotor resistance; ds the d-axis stator flux; qs the q-axis stator flux; dr the d-axis rotor flux; qr the q-axis rotor flux; the angular speed of the synchronous rotating reference frame; r the rotor angular speed; Ls the stator inductance; Lr the rotor inductance; Lls the stator leakage inductance; Llr the rotor leakage inductance; Lm the mutual inductance; and p the number of pole pairs. Next, the active power and reactive power output from the stator and rotor side of DFIG can be derived from Eqs. 9 and 10, and can be expressed as:
+
jsdq + -
isdq
usdq
dsdq /dt
-
jLls
Lm
-
ugdq
ufdq
igdq Rfg (c)
drdq /dt (a)
jsLfg
j(-r)rdq R r - + +
+
+
jLlr
+
GSC
irdq
+
urdq
-
-
iloss
Cdc
igdc
RSC
irdc
-
udc +
(b)
Figure 11. Equivalent circuit of DFIG: (a) WRIG generator; (b) Power electronic converters and DC-link; and (c) grid filter.
WIND TURBINE-GERNERATOR CONTROL The block diagram for the overall control stategies of DFIGWECS is shown in Fig. 12, including two parts: the first part is the electrical control system of DFIG, which includes control of the RSC and the GSC. The objective of the RSC is to allow the DFIG wind turbine for decoupled control of active and reactive power or speed, whereas the objective of the GSC is to keep the DC-link voltage at given value in defiance of the magnitude and direction of the rotor power. The second part is the mechanical control system of the wind turbine having the main objective to be the capture of wind power maximization and minimization of transient low speed shaft loads.
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com Transformer i l
Turbine
is m J Tm
Grid
Greabox
us
Te Jg
Dwt
D K
T
ug
WRIG
Prc ,Qrc
Pdc ,Qdc
Dg
VWind
T
wt
Pg ,Qg
Pfc ,Qfc
r
uf Cdc
Twt
udc
ir ur
Pl ,Ql
Ps ,Qs
Jwt
rated r
Active Crowbar
RSC control
ig
Rfg ,Lfg
GSC control
r ref
Qs.ref (Ps.ref)
Wind Turbine Control
Qs (Ps)
Udc.ref Qref
Qg
Figure 12. Block diagram for WECS-DFIG.
different wind speeds. When the wind speed increases to the value larger than the rated one (at line CD, as shown in Fig. 6b), the pitch control is activated to restrain the rated over power production, meanwhile the turbine speed is maintained at rated speed. r.ref is set at the rated speed of the generator, as is shown in Fig. 6c (at point C @ D).
Pitch Angle Control The pitch angle control is used to change blade pitch angle when the wind speed is higher than rated wind speeds, so that the production power of the wind turbine is limited even though the wind speed exceeds rated speed, as shown in Fig. 13 [23]. In addition, from Fig. 6 shown that Cpmax(,) = 0.48, which corresponds to the tip speed ratio = 8.1 and pitch angle = 0. The mechanical torque can be obtained from the wind turbine that it drives the generator is as shown in Eq. (6), resulting in K = (1/2) R2Cpmax(,) constant. Therefore, the mechanical power can be obtained as follows: (15) Pm KVw3 .
Rotor Side Converter Control The RSC control scheme is shown in Fig. 14, including the inner and outer control loops. The outer control loops have two PI controllers, which are used to regulate the stator reactive and active power independently, whereas the inner ones have two PI controllers, which are used to regulate the daxis and q-axis rotor currents independently [24]. Because the system is symmetrical, the parameters of the PI controllers are the same for the d-axis and q-axis rotor current loops and the reactive and active power loops. For the purpose of DFIG-WECS control, the d-axis of the synchronous reference frame along the stator linkage i.e qs 0 and ds s or the stator voltage i.e uds 0 and uqs us is most often employed, as shown in Fig. 15. Therefore, Eqs. (6) and (8)(11) show the relationship between iqr, idr and r, Qs in the synchronous rotating dq reference frame with d-axis oriented along the stator-flux vector position is employed, i.e s, uds 0, and qs 0, assuming the stator flux is constant, neglecting the stator resistance and the damping factor, therefore we have: 2 Ls 2 J d r iqr ( Tm ), 3 pLm ds p dt (17) 1 1 2Ls Lr dQs idr ((udr (s r )Lr iqr ) ). Rr ds 3s Lm dt
Mechanical Servo-system
max
r
kP
+-
r .ref
min
kI S
ref
+-
1 T
d max dt d min dt
max 1 S
min
Figure 13. Schematic diagram of the pitch angle controller for DFIG-WECS.
As can be seen in Fig. 6b,c the power-speed characteristic curves denote the captured energy from the wind. When the wind speed ranges between the cut-in wind speed and the low limit wind speed at line AB, as shown in Fig. 3b, the rotor reference speed of the generator is set at a minimum value 0.7 p.u., as shown in Fig. 6c. When the wind speed is greater than the low limit wind speed and smaller than the rated wind speed at line BC, as shown in Fig. 6b, the generator is operated in the variable speed model at line BC, as shown in Fig. 6c, and then the generator rotor reference speed is set as: P Tm r .ref 3 m , (16) Kotp Kotp where Kopt (1 / 2)(R2 / 3opt )Cpmax (, ) is the optimal constant of turbine. The pitch angle is kept constant at opt that is usually equal to zero, while is adjusted to opt according to
2987
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com Turbine Blade
DFIG t
r
Gear Box
Grid
Transformer
WRIG
~
CTs
Wind
r
RSC
dt
-
r .ref
e
r
PCC
R fg
VTs
L d )iqr (s r )( m ds Lr idr ), dt Ls
udr ( Rr Lr
d )idr (s r )Lr iqr , dt
(20)
CTs
abc
+
Figure 13
GSC
L fg
uqr ( Rr Lr
PWM
jslip
abc
idr iqr
e
slip
uqr .ref +
k Iiqr S
Lr iqr
ids iqs r
q
uds uqs
d
-
ir
us
s
slip
slip Lr iqr udr
-
-
+
e j s
d / dt
idr .ref 1 Rr
+
s
r
slip
idr
+
-
+
slip
k Iidr S
k Pidr
iqr .ref 2 pLs 3Lmds
Tm
-
qr
udr .ref +
+
i
abc
+
k Piqr
s
e j s
jslip
+
Lm Lr idr ) slip ( s Ls
PLL
abc
irq
1
ds
k Pr
k I r S
+
S
+
-
r
k IQs
-
k PQs
r .ref
Qs.ref
s r
ird e s
r
r
s
s
s
3 Qs (uqs ids uds iqs ) 2
Figure 15. Stator/grid flux reference frame.
Figure 14. Control scheme of the RSC.
where k P and k I are the proportional and integral gains of
As can be observed from Eq. (20), there is the cross-coupling item (s-r)σLridr in the q-axis rotor voltage equation, whereas there is another cross-coupling item (s-r)σLriqr in the d-axis rotor voltage equation. Therefore, these two equations are coupled and the traditional linear controllers cannot be used. However, through the exact linearization method, this equation can be linearized by putting the other terms to one side, we have: k Ii d qr ( Rr Lr )iqr (k Pi )(iqr .ref iqr ), qr dt S (21) k Ii d dr ( Rr Lr )idr (k Pi )(idr .ref idr ), dr dt S where k Pi and k Ii are the proportional and integral gains of
the rotor speed controller, respectively, k PQ and k IQ are the
the q-axis RSC current controller, respectively, k Pi
The control plant described by Eq. (17) is nonlinear due to the presence of terms dr/dt and dQs/dt. To use the linear controllers that include integrations, we must calculate the derivative terms. The nonlinear equation become linear when all the nonlinear terms are moved to one side of the equation, we have: k I 2 J d r (k P r )(r .ref r ), r p dt S (18) k I Qs 2Ls Lr dQs (k PQ )(Q s.ref Q s ), s 3s Lm dt S r
r
s
qr
s
dr
proportional and integral gains of the RSC reactive power controller, respectively, and S is the Laplace’s operator. The dq-axis rotor reference currents can be obtained, when passed through the proportional and integral gains (PI), we have: k 2 Ls iqr .ref ((k Pr I r ) (r .ref r ) Tm ), 3 pLm ds S idr .ref
and k Ii
dr
are the proportional and integral gains of the d-axis RSC current controller, respectively. The dq-axis rotor current references can be obtained, when passed through the proportional and integral gains, we have: k Iiqr uqr .ref (k Piqr )(iqr .ref iqr ) S PIq rotor current
PIspeed
1 ((udr (s r )Lr iqr ) Rr
qr
(s r )(
(19)
udr .ref (k Pidr
k IQs 1 (k PQs )(Q s.ref Q s )), ds S
Lm ds Lr idr ), Ls
(22)
k Iidr )(idr .ref idr ) S
PId rotor current
PIstator reactive
(s r )Lr iqr ,
where the value of r.ref is generated by the wind turbine control level and Qs.ref is the reference value of the stator reactive. As shown from Eq. (8), the relationship between uqr, udr and idr, iqr in the synchronously rotating dq reference frame with daxis oriented along the stator-flux vector position, is employed, i.e s, uds 0, qs 0, is:
As known, the whole system might be able to work for a wide range of parameters. Therefore, in order to obtain the good operation performance, the choice of the control parameters of PI controllers is very important. Therefore, some methods for using to design the PI-controllers have proposed, such as root locus [25], pole-placement [26], Ziegler-Nichols tuning [27], Bode [28], internal model control [29] and Butterworth polynomial [30]. In this paper, the Butterworth polynomial 2988
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com method is re-called to calculate the eigenvalues uniformly in the left half s-plane on a circle center at the origin with radius o, as shown Fig. 16.
Similarly, by comparing the denominator coefficients in the last expression (25) with the corresponding transfer function in Eq. (23), we have: ( Rr Lr S )iqr (k Piqr
Imaginary
S1
o
( Rr Lr S)idr (k Pidr
*
Eq. (27) changes into: iqr
Real
S2
iqr .ref
k Iiqr S
)(iqr .ref iqr ),
k Iidr )(idr .ref idr ). S
(27)
1 ( Sk Piqr k Iiqr ) Lr , 1 1 S2 S ( Rr k Piqr ) k Iiqr Lr Lr
(28) 1 ( Sk Pidr k Iidr ) idr Lr . idr .ref S 2 S 1 ( R k ) 1 k r Pidr Iidr Lr Lr By comparing denominator coefficients in Eq. (28) with the corresponding transfer functions in Eq. (23), we have:
*
Figure 16. Pole locations second order denominator for Butterworth polynomial
k Pidr k Piqr Lr 2oidqs Rr , 2 k Iidr k Iiqr Lr oi , dqs
The transfer function to a second order denominator of the Butterworth polynomial method is expressed as: (23) S 2 2S o o2 0. Therefore, the parameters of the PI controllers to RSC are determined based on the transfer function (23).
(29)
where oidqs is the bandwidth of the current controller. Grid Side Converter Control The GSC is connected between the DC-link and the grid via the filter, as shown in Fig. 12. The major objective is to maintain the DC-link voltage at a given value and to regulate the reactive power flow between the GSC and the grid. The GSC is usually operated at unity power factor, but it can be used for voltage support during the grid fault by injecting reactive power into the grid. The vector-oriented control was chosen for the GSC control with a reference frame oriented along the grid voltage vector position, as shown in Fig. 17. Thanks to this, it can independently control the active and reactive current between the grid and the GSC. Similar to RSC control, The GSC has the PI controllers that are used to regulate the DC-link voltage, reactive power and current control loops, as illustrated in Fig. 17. The equivalent circuit of the grid filter is shown in Fig. 11c. The balance voltage across the grid filter in the synchronous rotating dq reference at s is:
Determining the Parameters of the PI Controllers to RSC From Eq. (18), we have: k 2J S r (k Pr I r )(r .ref r ), p S (24) k IQs 2Ls Lr SQs (k PQs )(Q s.ref Q s ). 3s Lm S Equation (24) changes into: p (S k Pr k I r ) r 2J pk pk r .ref S 2 S Pr I r 2J 2J 1 (S k PQs k IQs ), (25) 2 Ls Lr Qs 3 s Lm . 1 1 Q s.ref S 2 S k PQs k IQs 2 Ls Lr 2 Ls Lr 3 s Lm 3 s Lm By comparing the denominator coefficients in the first expression (25) with the corresponding transfer functions in Eq. (23), we have: 2J k Pr 2or , p (26) 2J 2 k I r or , p
udg udf ( R fg L fg uqg uqf ( R fg L fg
d )idg s L fg iqg , dt d )iqg s L fg idg , dt
where Rfg the grid side filter resistance; Lfg the grid filter inductance; udf the d-axis grid filter voltage; uqf the q-axis grid filter voltage; udg the d-axis grid voltage; uqg the q-axis grid voltage; idg the d-axis grid filter current; iqg the q-axis grid filter current; and
where or is the bandwidth frequency of speed controller.
2989
(30)
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com the electrical angular speed of the grid voltage.
s
udg .ref (k Pi
Turbine Blade
dg
DFIG
t
r
Gear Box
Grid
Transformer
L fg
RSC
GSC
uqg .ref (k Pi
PCC
R fg
VTs
qg
CTs
U dc
abc
+
-
ug .ref
e j s
ug .ref
e j s -
k Ii
qg
S
(32) )(iqg .ref iqg ) s L fg idg uqf .
s qg
iqg .ref
k I dc
k PQg
S
S
U
Q
2 dc .ref
the active and reactive power flow between the GSC and the grid can be obtained as follows: 3 Pg udg idg , 2 (33) 3 Qg udg iqg . 2 Next, neglecting the harmonics and losses in the resistance and converter, we have as [24]: 3 U dc idcg udg idg , 2 3 idcg (mdg idg mqg iqg ), (34) 4 3 idcr (mdr idr mqr iqr ). 4 Therefore, the equivalent circuit of the DC-link is shown in Fig. 11b. The equation of dynamic behavior of the capacitor can be calculated as [21,24,31]: d 3 Cdc U dc (mdr idr mqr iqr ) dt 4 (35) 3 (mdg idg mqg iqg ) igdc irdc , 4 where Cdc is the DC-link capacitance, Udc is the DC-link voltage, mdr = 2udr.ref/Udc and mqr = 2uqr.ref/Udc are the modulation indexes of RSC in the dq-axis, respectively, and mdg = 2udg.ref/Udc and mqg = 2uqg.ref/Udc are the modulation indexes of GSC in the dq-axis, respectively. The linear dynamic of the system is replaced by using the PI controller, and can be expressed as:
k IQg
+
-
2 dc
uds uqs
i
+
U
e j s
2 3udg
2 3udg
k Pdc
Next, the active and reactive power flow between the GSC and the grid can be calculated as follows: 3 Pg (udg idg uqg iqg ), 2 (32) 3 Qg (uqg idg udg iqg ). 2 Because the d-axis of the reference frame is aligned to the grid voltage vector position, as shown in Fig. 18, uqg is zero. Thus,
d / dt
S
+
idg .ref
s
abc
fg dg
k Iidg
k Pidg
S
+
dg
-
i
k Iiqg
s
-
k Piqg
PLL
s i i dg qg
L i
-
+
s L fg iqg
-
dg
uqg .ref
udg .ref
+
u
abc
PWM
r
Q g
g.ref
Figure 17. Control scheme of the GSC.
q
ig
igq ug
s
d igd
s
Figure 18. Grid voltage reference frame.
Similar, according to Eq. (30), the linear dynamic of the system is replaced by using the PI controller, and can be expressed as: k Ii d dg ( R fg L fg )idg (k Pi )(idg .ref idg ), dg dt S (31) k Ii d qg ( R fg L fg )iqg (k Pi )(iqg .ref iqg ), qg dt S where k Pi and k Ii are the proportional and integral gains of dg
)(idg .ref idg ) s L fg iqg udf ,
PIq-grid current
Figure 13
r .ref
dg
S
PId -grid current
~
WRIG
Wind
k Ii
dg
the d-axis GSC current controller, respectively and k Pi and qg
Cdc
k Ii are the proportional and integral gain of the q-axis GSC qg
kI d U dc (kPdc dc )(U dc.ref U dc ), dt S
(36)
where k Pdc and k I dc are the proportional and integral gains of
current controller, respectively. Therefore, the d-axis grid reference voltages can be obtained, when passed through the proportional and integral gains, we have:
the DC-link controller, respectively. Therefore, the d-axis grid reference current can be obtained, when passed through the proportional and integral gains, we have: kI 1 4 idg .ref ( ((k Pdc dc )(U dc.ref U dc ) mdg 3 S PIdc (37) 3 (mdr idr mqr iqr )) mqg iqg ), 4 2990
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com Next, taking the derivative of two sides of the last expression (33) according to time, we have: d 3 d Qg udg iqg . (38) dt 2 dt By substituting the last expression (32) into Eq. (38), we have: dQg 3 udg (uqf s L fg idg R fg iqg ). (39) dt 2 L fg
k Pdc Cdc 2odc , 2 . k I dc Cdc odc
Finally, from Eq. (40), we have: k IQ g L fg SQg (k PQ )(Qg .ref Qg ). g S Eq. (48) changes into: (k PQ S k IQ ) Qg g g . k PQ k IQ Qg .ref g g 2 (S S ) L fg L fg
The linear dynamic of the system is replaced by using the PI controller, and can be expressed as: k IQ dQg g (40) L fg (kPQ )(Qg .ref Qg ), g dt S where k PQ and k IQ are the proportional and integral gains of g
the reactive power controller, respectively. Therefore, the q-axis grid reference current can be obtained, when passed through the proportional and integral gains, we have: k IQ 1 2 1 g iqg .ref ( (k PQ )(Qg .ref Qg ) g R fg 3 udg S (41)
CASE STUDIES AND RESULTS In order to estimate the performance of DFIG when connecting to the grid, the implemented system of a 2.0 MW575 kV DFIG-WCES together with the network which has been simulated, as shown in Fig. 12, in which the components of mode are built by using PSCAD/EMTDC software. The grid voltage and frequency are 25 kV and 50 Hz, respectively. The parameters of the DFIG-WCES system and PI controllers are listed in Appendix. The DFIG-WCES is investigated with the following different scenarios.
(uqf s L fg idg )).
Determining the Parameters of the PI Controllers to GSC From Eq. (41), we have: k Ii dg R fg idg L fg Sidg (k Pi )(idg .ref idg ), dg S (42) k Ii qg R fg iqg L fg Siqg (k Pi )(iqg .ref iqg ). qg S Eq. (42) changes into: 1 ( Sk Pi k Ii ) dg dg idg L fg , idg .ref S 2 S 1 ( R k ) 1 k fg Pidg I idg L fg L fg (43) 1 ( Sk Pi k Ii ) qg qg iqg L fg . iqg .ref S 2 S 1 ( R k ) 1 k fg Piqg I L fg L fg iqg
Case 1: Response to normal condition In order to demonstrate the ability of the model to reproduce the wind turbine when correcting the grid, the steady state condition test was created. The wind turbine was operated with a constant wind speed 12 m/s that was chosen to be the rated value. The simulation results of the studied DFIGWCES, operating at constant wind speed of 12 m/s and under the balanced grid voltage, are plotted in Fig. 19. The DFIG-WECS connected to the grid under the normal condition as shown in Fig. 19a and it is operating at the synchronous speed corresponding to the rated wind speed (12 m/s). Fig. 19c,d presents the behavior of the DFIG-WECS in terms of active and reactive supplied into the grid, respectively. It can be observed that the active and reactive current exchanges are reached the rated value 1.0 and 0.0 p.u. at time 0.2 and 0.3 sec after the DFIG is connected to the grid, respectively. Fig. 19b shows the stator current supplied by the DFIG, this current is directly related to out read power of the generator, stabilized at time 0.1 sec. Fig. 19e plots the DC-link voltage. As can be observed from this figure, DC-link voltage is maintained constant at 1.5 sec. The rotor voltage and current of generator is also stabilized after time 0.055 and 0.1 sec, respectively, as shown in the Figs 19g,h. Fig. 19h plots the pitch angle. As can be observed from this figure that the pitch angle is active to maintain the rotor speed at rated value 1.0 p.u., settles after time 0.3 sec and close to 0.75 degrees, as shown in Fig. 19f. Thus, the out power of generator is maintained at the rated value, as shown in Fig. 19c.
By comparing the denominator coefficients in Eq. (43) with the corresponding transfer function in Eq. (23), we have: qg
k Pi k Ii L fg oi2 dqg , dg
(44)
qg
Next, Eq. (36), we have: Cdc SU dc (kPdc
Eq. (45) changes into:
kI dc S
)(U dc.ref U dc ).
(49)
g
PIgrid reactive
dg
(48)
By comparing the denominator coefficients in Eq. (49) with the corresponding transfer function in Eq. (23), we have: k PQ L fg 2oQg , g (50) 2 k IQ L fg oQ . g
g
k Pi k Pi L fg 2oidqg R fg .
(47)
(45)
1 (S k Pdc k I dc ) U dc C dc . (46) k Pdc k I dc U dc.ref 2 S S Cdc Cdc By comparing the denominator coefficients in Eq. (46) with the corresponding transfer function in Equation (23), we have:
2991
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com 1.0 0.75
β [Deg.]
1.0
us [p.u.]
0.5
0.25 0.5
(k)
1.0 (a)
0.0
0.05
0.10
0.15
0.30
0.25
0.20
0.25
0.30
0.35
0.40
0.35
is [p.u.]
0.0 -0.5
0.05
0.10
0.15
0.05
0.10
0.15
0.20 Times [s]
0.25
0.30
0.35
0.40
Times [s]
0.75
0.0
(c)
1.0
Qs [p.u.]
0.0
-0.5
0.05
0.10
0.15
0.20 Times [s]
0.25
0.30
0.35
0.40
0.05
0.1
0.15
0.2 Times [s]
0.25
0.3
0.35
0.40
2.5
Udc [p.u.]
2.0
1.5 1.0 0.5
(e) 0.0 0.0
0.2 Times [s]
0.3
0.25
0.40
0.35
The simulation for this case is performed to confirm the steady state performance of the grid-connected DFIG-WECS under the variable wind. The response of the DFIG-WESC with the variable wind speed from 8 m/s to 13 m/s is plotted in Fig. 20. Fig. 20a represents the variable wind speed profile that increased from 8 to 13 m/s at time t 18 to 20 sec, respectively. The corresponding mechanical power and aerodynamic torque are shown in Fig. 20b,c. It can be observed that during the variable wind speed with time t 18.6 to 20 sec, the generator operates at the wind speed 8 m/s, this wind speed value corresponds to the hypo-synchronous operation mode of the DFIG. The generator is changed from the hypo-synchronous operation mode to the hyper-one during the time from t 20 to 22 sec, and after, operates at the hypo-synchronous operation mode. The corresponding rotor speed, reactive power, active power, and electromagnetic torque are shown in Figs. 20hm. The DC-link voltage response is plotted in Fig. 20n. Fig. 20dg shows the response of the corresponding stator and rotor voltages and currents. Therefore, the results in this case show that, having small transients in the DFIG-WESC occurred.
1.5
(d) -1.0 0.0
0.15
0.1
Case 2: Response to wind speed variable
(b)
-0.75 0.0
0.05
Figure 19. Response performance of DFIG-WECS under steady state condition: (a) Stator voltages; (b) Stator currents; (c) Stator active power; (d) Stator reactive; (e) DC-link voltage; (f) Rotor speed; (g) Rotor voltages; (h) Rotor currents; and (k) Pitch angle.
0.5
-1.0 0.0
0 0.0
0.40
0.20 Times [s]
1.0
Ps [p.u.]
0.5
0.0
1.1
1.0
r [p.u.]
15
Wind Speed [m/s]
0.9
0.8 (f) 0.0 0.0
0.05
0.1
0.15
0.2 Times [s]
0.25
0.3
0.35
0.40
13 11 9 7
1.0 (a) 5 18.0
0.0
-0.5 (g)
18.5
19.0
19.5
20 Times [s]
20.5
21.0
21.5
22.0
1.2
Wind power [p.u.]
Ur [p.u.]
0.5
-1.0 0.0
0.05
0.1
0.15
0.2 Times [s]
0.25
0.3
0.35
0.40
1.0 0.8 0.6 0.4
1.5 (b)
0.5
Aerodynamic torque [p.u.]
Ir [p.u.]
1.0
0.0
-0.5 -1.0 (h) -1.5 0.0
0.05
0.1
0.15
0.2 Times [s]
0.25
0.3
0.35
0.40
Figure 19. (Cont.)
0.3 18.0
18.5
19.0
19.5
20.0
20.5
21.0
18.5
19.0
19.5
20.0
20.5
21.0
22.0
-0.3 -0.4 -0.5 -0.6
(c) -0.718.0
Figure 20. (Cont.)
2992
21.5
-0.2
21.5
22.0
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com
Case 3: Response to grid voltage sage
Stator voltage [p.u.]
1.0
The scenario in this case is performed to demonstrate the model’s response ability under the voltage sag. The wind turbine operated with a rated wind speed 12 m/s. Considering that the voltage at the point of common coupling (PCC) is gradually dropped from 1.0 to 0.5 p.u. at 0.2 sec, as shown in Fig. 21a. As can be shown from Fig. 21 that when the voltage at PCC suddenly changes, the stator and rotor currents increase, as shown in Fig. 21b,h. The stator active power suddenly oscillates and then it recovers to its rated value, as seen in Fig. 21c. As can be observed from Fig. 21d, the stator reactive power suddenly increases. However, the control scheme for the grid-side converter and then tries to control it backs to its reference value; normally this reactive power is controlled at value zero. The grid voltage sage occurs, the DC-link voltage is oscillated and then it backs to its reference value after clearing the grid voltage sage as shown 21e. The rotor speed is also maintained constant to its rated, as shown in Fig. 21f and the rotor voltage is also maintained as shown in Fig. 21g.
0.5 0.0 0.5 1.0
(d)
18.0
18.5
19.0
19.5
22.0
20.5
21.0
21.5
20.0
20.5
21.0
21.5
22.0
20.0
20.5
21.0
21.5
22.0
20.0
Stator current [p.u.]
1.0 0.5
0.0
-0.5
(e) -1.0 18.0
18.5
19.0
19.5
Rotor voltage [p.u.]
1.0 0.5
0.0
-0.5
(f)
-1.0 18.0
18.5
19.0
19.5
1.0
1.0
0.5
0.5
Us [p.u.]
Rotor current [p.u.]
1.5
0.0
-0.5 -1.0
(g)
-1.5 18.0
0.0 0.5
18.5
19.0
19.5
20.0
20.5
21.0
21.5
1.0
22.0
(a)
0.0
0.25
0.25
0.30
0.35
0.40
0.20
0.25
0.30
0.35
0.40
0.15
0.20 Times [s]
0.25
0.30
0.35
0.40
0.15
0.20 Times [s]
0.25
0.30
0.35
0.40
0.15
0.2 Times [s]
0.10
0.15
0.05
0.10
0.15
0.05
0.10
0.05
0.10
0.05
0.20 Times [s]
1.0
-0.25
0.5
-0.5
Is [p.u.]
Ps and Qs [p.u.]
0.0
-0.75 -1.0 -1.25
(h) -1.5 18.0
-0.5 18.5
19.0
19.5
20.0
20.5
21.0
21.5
22.0
(b)
-1.0 0.0
Generator speed [p.u.]
1.35
Times [s]
1.5
1.2
Ps [p.u.]
0.8
0.4
(k) 0.0 18.0
18.5
19.0
19.5 20.0 Times [s]
20.5
21.0
21.5
0.75
0.0
(c)
22.0
-0.75 0.0
0.0
1.0
-0.2 -0.4
Qs [p.u.]
Electromagnetic torque [p.u.]
0.0
-0.6
-0.8
(m)-1.0 18.0
18.5
19.0
19.5 20.0 Times [s]
20.5
21.0
21.5
22.0
-0.5
(d) -1.0 0.0
1.25
2.5
1.0
2.0 0.75
Udc [p.u.]
DC-link Voltage [p.u.]
0.0
0.5 0.25
(n) 0.0 18.0
18.5
19.0
19.5
20.0 Times [s]
20.5
21.0
21.5
1.5 1.0 0.5
22.0
(e) 0.0 0.0
Figure 20. The dynamic performance of DFIG-WCES in case of the variable wind speed: (a) Wind speed; (b) Wind power; (c) Aerodynamic torque; (d) Stator voltages; (e) Stator currents; (f) Rotor voltages; (g) Rotor currents; (h) Stator reactive and active power; (k) Generator speed; (m) Electromagnetic torque; and (n) DC-link voltage.
0.05
0.1
0.25
Figure 21. (Cont.)
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com 1.1
1.0
0.0
Qs [p.u.]
r [p.u.]
1.0
0.9
-0.5
0.8
(d) -1.0 0.0
(f) 0.0
0.05
0.1
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0.2 Times [s]
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0.20 Times [s]
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0.2 Times [s]
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2.0
Udc [p.u.]
0.5
Ur [p.u.]
0.15
0.25
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0.05
2.5
1.0
0.0
1.5 1.0
-0.5 0.5
(g)
-1.0 0.0
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0.1
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0.2 Times [s]
0.25
0.3
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(e) 0.0 0.0
0.40
1.5
0.05
1.1
1.0
r [p.u.]
Ir [p.u.]
1.0
0.5 0.0
0.9
-0.5 -1.0 (h) -1.5 0.0
0.8 (f)
0.05
0.1
0.15
0.2 Times [s]
0.25
0.3
0.35
0.40
0.0
Figure 21. Response performance of DFIG-WECS under voltage sag condition: (a) Stator voltages; (b) Stator currents; (c) Stator active power; (d) Stator reactive; (e) DC-link voltage; (f) Rotor speed; (g) Rotor voltages; and (h) Rotor currents.
1.0
Ur [p.u.]
0.5
-0.5
Case 3: Response to grid voltage swell The simulation of this case was done to demonstrate the
(g)
model’s response ability under the voltage swell. The wind turbine operated with a rated wind speed 12 m/s. In this case, considering that the voltage at the point of common coupling (PCC) is gradually dropped from 1.0 to 1.2 p.u. at 0.2 sec, as shown in Fig. 22a. The response of the proposed model for grid voltage swell is plotted in Fig. 22. As can be seen from this figure that the stator current as well as rotor current decreases. The active and reactive powers and DC-link are oscillated and then they back to its initial value.
Ir [p.u.]
1.0
Us [p.u.]
0.0
-1.0 (h) -1.5 0.0
Figure 22. Response performance of DFIG-WECS under Voltage swell condition: (a) Stator voltages; (b) Stator currents; (c) Stator active power; (d) Stator reactive; (e) DC-link voltage; (f) Rotor speed; (g) Rotor voltages; and (h) Rotor currents.
Case 4: Response to frequency change
In order to verify the response of the proposed model for frequency change, this simulation was done with frequency change from rated frequency 50.0 to 46.0 Hz t 0.2 to 0.3 sec, respectively. Fig. 23 plots the detail of the response of DFIG-WECS. It can be observed from this figure, show that the proposed model is not responding when the supply frequency is changed. It clearly means that the optimal control strategies need to be used to enhance the response ability for the system.
0.0
0.5 1.0 0.05
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is [p.u.]
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1.0
(a)
0.0
0.0 -0.5
(b)
-1.0 0.0
1.0
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0.20
Times [s]
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Ps [p.u.]
us [p.u.]
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0.0
0.5 1.0 (a)
0.0
-0.75 0.0 (c)
0.0
0.05
0.10
0.15
0.20 Times [s]
0.25
Figure 23. ( Cont.) 0.05
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0.20 Times [s]
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Figure 22. (Cont.)
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com technique; the PI controllers are designed based on the Butterworth polynomial method. From simulation analyses, it can be concluded that the proposed model is a simulation tool used as a test-bench for academic in order to model, study, and analyze the transient and grid interface requirements, and especially lead with the challenge for the distributed generators (DGs) integration into exiting electric grid and offshore, micro-grid, standalone systems. Furthermore, the proposed model has been successfully integrated into the renewable energy conversion systems and it can also serve as useful preparatory exercises for power system junior engineers in this renewable energy conversion field.
1.0
is [p.u.]
0.5 0.0 -0.5 (b)
-1.0 0.0
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Times [s]
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Ps [p.u.]
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(c) 1.5
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Qs [p.u.]
0.5
APPENDIX
0.0
Parameters
Value
-0.5 (d) -1.0 0.0
0.15
0.20 Times [s]
0.1
0.15
0.2 Times [s]
0.25
0.3
0.35
0.40
0.05
0.1
0.15
0.2 Times [s]
0.25
0.3
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0.40
0.05
0.1
0.15
0.2 Times [s]
0.25
0.3
0.25
0.30
0.35
Prated Urated Irated rated n J Cf Rs Rr Lls Llr Lm Ng Rf Lf Udc C fsw sw
0.40
0.10
0.05
Udc [p.u.]
1.5
1.0
1.5 (e) 0.0
0.05
r [p.u.]
1.1
1.0
0.9 (f) 0.0
1.0
ur [p.u.]
0.5
0.0
-0.5 (g)
-1.0 0.0
0.35
0.40
o
1.5 1.0
the rated power the rated voltage the rated current the rotor rated speed the stator/rotor turns ratio the inertia constant the friction factor the stator resistance the rotor resistance the stator leakage inductance the rotor leakage inductance the mutual inductance the gear ratio the resistance of grid filter the inductance of grid filter the DC-link rated voltage the capacitor in the DC-link the switching frequency the switching bandwidth frequency the bandwidth of speed controller
2 MW 575 V 1505 A 1.1 p.u. 0.4333 0.5 p.u. 0.01 p.u. 0.00706 p.u. 0.005 p.u. 0.0.171 p.u. 0.15 p.u. 3.5 p.u. 98 0.003 p.u. 0.3 p.u. 1200 V 0.03 F 2 kHz 2fsw
sw /100
sw /1000
Vw _ cut in
In this paper, a complete model for doubly fed induction generator based on wind energy conversion system (DFIGWECS) has been proposed and whole model is built in PSCAD/EMTDC. The control scheme used the vector control
Vw _ cut out
the cut-out wind speed
25 m/s
Vw _rated
the wind rated speed
12 m/s
Vw _lower
the lower limit of the wind speed 7 m/s
Ir [p.u.]
CONCLUSION
the bandwidth of stator reactive controller the bandwidth of stator current controller the bandwidth of grid current controller the bandwidth of DC-link voltage controller the bandwidth of grid reactive controller the cut-in wind speed
oQs
0.5 0.0
oidqs
-0.5 -1.0 (h) -1.5 0.0
0.05
0.1
0.15
0.2 Times [s]
0.25
0.3
0.35
oidqg
0.40
Figure 23. Response performance of DFIG-WECS under frequency change condition: (a) Stator voltages; (b) Stator currents; (c) Stator active power; (d) Stator reactive; (e) DC-link voltage; (f) Rotor speed; (g) Rotor voltages; and (h) Rotor currents.
odc
oQg
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sw/10 sw/10 sw /100 sw /100 4 m/s
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 11 (2017) pp. 2981-2996 © Research India Publications. http://www.ripublication.com [15]. Miller N. W., Price W. W., and Sanchez-Gasca J. J., 2003, Dynamic Modeling of GE 1.5 and 3.6 Wind TurbineGenerators, General Electric International, Power Systems Energy Consulting: Schenectady, NY, USA. [16]. Aguglia D., Cros J., Viarouge P., Wamkeue R., 2011, Optimal selection of drive components for doubly-fed induction generator based wind turbines. INTECH Open Access Publisher. [17]. Fan L., Kavasseri R., Miao Z. L. and Zhu C., 2010, “Modeling of DFIG-based wind farms for SSR analysis,” IEEE transactions on Power Delivery, 25(4), pp. 20732082. [18]. Iov F., Hansen A. D., Sorensen P. and Blaabjerg F., 2004, Wind Turbine Blockset in Matlab/Simulink, Aalborg University, Aalborg, Denmark. [19]. Datta R. and Ranganathan V. T., 2002, “Variable-speed wind power generation using doubly fed wound rotor induction machine-a comparison with alternative schemes,” IEEE Transactions on Energy Conversion, 17(3), pp. 414421. [20]. M. G. Simoes and F. A. Farret, 2011, Alternative energy systems: design and analysis with induction generators, CRC press. [21]. Krause P. C., Wasynczuk O., Sudhoff S. D. and Pekarek S., 2013, Analysis of electric machinery and drive systems. John Wiley & Sons, In., Hoboken, New Jersey, Canada. [22]. Jazaeri M., Samadi A. A., Najafi H. R., NorooziVarcheshme N., 2012, “Eigenvalue Analysis of a Network Connected to a WindTurbine Implemented with a DoublyFed Induction Generator (DFIG),” Journal of Applied Research and Technology , 10(5), pp. 791811. [23]. Xie D., Xu Z., Yang L., Ostergaard J., Xue Y. and Wong, K. P. A. 2013, “Comprehensive LVRT control strategy for DFIG wind turbines with enhanced reactive power support,” IEEE Transactions on Power Systems, 28(3), pp. 33023310. [24]. Pena R., Clare J. C. and Asher G. M., 1996, “Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation,” IEE Proceedings Electric Power Applications, 143(3), pp. 231241. [25]. R. B. Burns, 2011, Advanced control engineering. Butterworth-Heinemann, Linacre House, Jordan Hill, Oxford. [26]. Lewis P. H. and Yang C., 1997, Basic control system engineering, Prentice Hall, New Jersey. [27]. Ziegler J. G. and Nichols N. B, 1942, “Optimum settings for automatic controllers,” Transactions of the ASME, 64(4), pp. 759768. [28]. R. N. Bateson, 1996, Introduction to control system technology, Prentice Hall, New Jersey. [29]. Levine W. S., 2000, Control system fundamentals, CRC Press, Boca Raton. [30]. Gan Dong, 2005, Sensorless and Efficiency Optimized Induction Machine Control with Associated Converter PWM Modulation Schemes. Ph.D. dissertation, Tennessee Technological University. [31]. Vas P., 1998, Sensorless vector and direct torque control, Oxford University Press, New York.
ACKNOWLEDGEMENTS The authors sincerely acknowledge the financial support provided by Industrial University of Ho Chi Minh City, Ho Chi Minh, Vietnam, and Quy Nhon University, Binh Dinh, Vietnam, for carrying out this work.
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